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Why?

8/29/2018

Another shooting. Two dead, 11 injured. Hardly big enough to interest the media these days. We’re more used to numbers like 49, 58, and 17. This time it was people participating in a football video game tournament. People having fun on their free time. People having the right to feel safe. People having the right to be safe.

But there is no safety any more, and I’m angry. Because there are steps that can be taken, and few with the courage to take them.

This is not going to be a rehash of the horrible events at Pulse, Vegas, Parkland and elsewhere. One cannot imagine the terror, the pain, the ongoing emotional stress inflicted on these innocents, and I weep for the victims who fell and the ones who survived.

We hear how never again do we want a mass shooting. No one argues with that, but such shootings, terrible as they are, don’t begin to tell the entire story. Every single day, thousands and thousands of times a year, there are shootings that are just as devastating to those struck by them. They are so common we barely give them a glance in the short newspaper blurb devoted to them, if they appear at all. But I’m tired of them.

I’m tired of suicide by gun. A handy gun almost always is lethal when a person’s situation becomes so desperate that living seems no longer feasible. Too bad the distraught individual never has the opportunity to change his or her mind, as often happens when less effective methods such as overdoses are employed.

I’m tired of guns coming into play in domestic disputes. How many have lost their lives because there is a gun readily available when uncontrollable anger takes over?

I’m tired of kids finding guns lying around and killing themselves and others. And I’m tired of the adults that facilitate it.

I’m tired of disputes that used to be settled by fists, black eyes, and loosened teeth now ending in a bullet through the head.

And I’m tired of justifying it all by kowtowing to the Second Amendment.

Does the Second Amendment guarantee the right to own an antitank missile, a bazooka, a torpedo, a Tomahawk missile or a tactical nuclear weapon? I hope most would agree not. I think most would agree not.

That means there is a line, a point where what is allowed by the Second Amendment stops and should not be crossed. So, to argue the Amendment permits semiautomatic rifles such as AK-47s is spurious. What is up for debate about the Amendment is where the line is, and it is not carved in stone that these semiautomatic weapons fall on the allowed side of that line.

By the way, when someone vows they need an AK-47 because he’s a hunter, I have to wonder what kind of coward pits such a weapon against some poor and unsuspecting animal.

Where is common sense these days? Why isn’t there as much allegiance to facts as there is to a few words created more than 240 years ago at a time far different from now?

The facts are simple. There are more guns in our country than ever before. There are more deaths by guns in our country than ever before. It’s not a reach to believe there’s a correlation.

Here are some simple questions. Why is concern about guns a political litmus test? Why isn’t protection of our citizens the utmost priority of all our “leaders?” Why is there so much money available to pressure legislators to foster the gun culture? Why are legislators willing to be bought?

One more question. Why do we allow it?

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I Am a Mathematician

8/25/2018

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I am a mathematician.

Can there be anything that gives a person more thrills in life?

What’s that? You say you can think of one or two possibilities.

Well, I may have to concede the point. But I’m hoping I can give a hint as to why someone might pursue my line of work.

I wasn’t always a mathematician, by the way. At one point, for too long a time in my career, I was an electrical engineer. I was a terrible electrical engineer. You’ve heard those wonderful stories about the scientist in his lab (or garage) developing circuits that would change the world. Apple comes to mind. I might be in the lab all right, but never did I change the world. In college I held the record for creating the largest short circuit in my school’s history.

Fortunately, as I was forming, so were computers and I found a niche in that area that allowed me to house and feed my family. And it was fun. But not fun enough. I didn’t have the knowledge to do things I wanted to do. I needed to learn mathematics, mathematics beyond what engineers learned.

One day, after seven long years of half-time school, full-time work, and double-time husband and father, I finally could say, “I am a mathematician.”

This perhaps is not the best phrase to utter at parties. If I’m speaking to someone and am asked what I do, the answer often is, “Oh.” And after a pause, “That was my worst subject.” And after another delay, “Well, it’s been nice meeting you, but I have to leave.” This is not all bad. When I’m in a discussion with someone who is boring me to tears, I make certain to mention my life’s work and once again I’m left to my own devices.

But when I’m with other mathematicians, no one thinks I’m strange. When one of us asks, “How many “n”s in innovation, everyone knows the person is really requesting how many come after the initial “i.” But a mathematician will answer, “three,” and the asker will respond, “Thank you.” I shudder at what you might be thinking.

So what is it that drives one to mathematics? Let me try to explain with the story of a now famous mathematician.

His name is Andrew Wiles. He proved Fermat’s Last Theorem. Most of us learned that 3 squared plus 4 squared is equal to 5 squared, that is, (3 x 3) plus (4 x 4) is equal to (5 x 5) (exponent is 2). There are lots of other triples of numbers (meaning positive integers such as 1, 2, 3, …) that satisfy this, like 5 and 12 and 13. But what if I asked for three numbers b, c, and d such that b cubed (exponent is 3) plus c cubed is equal to d cubed, that is, (b x b x b) plus (c x c x c) is equal to (d x d x d)? Pierre de Fermat, a giant in mathematical history, said there are no such numbers. In fact, he said there are no such numbers if the exponent is 4 or 5 or any integer bigger than 2, and he declared in a margin of a notebook he had a beautiful proof but didn’t have the space to include it there. Most doubt he did have a proof, because some of the best mathematical minds over centuries couldn’t prove it. Until Andrew Wiles.

Now in a world that’s going to pot, one might wonder why anyone would care. But, to a mathematician, his proof is a big deal, a really big deal. A deal big enough for a documentary to be produced showing the drama of its discovery. I have watched it many times and shown it to students. It depicts Wiles’ many year effort involving extremely advanced mathematics. He thought he had it proved, but then an error was found. Much more time went into discovering a fix. Finally, the proof was complete.

As I watched the story, I could feel the emotions sweeping Wiles. Great joy as he thought the proof done, intense misery at the discovery of the error, and ecstasy when the final proof was confirmed.

Most research mathematicians don’t deal with mathematics at the level of Wiles. But we still share the emotions.

To us it’s theorems, mathematical truths that have been proven by rigorous well-defined rules of argument, that we live by. What we do is think up some question no one knows the answer to. It’s the type of statement that has a yes or no answer. For example, if it’s Saturday today, will it be Saturday again in exactly seven days? Of course, in this case the answer is yes, so we have to find a question whose answer is unknown.

Then we try to figure out what the answer is. Usually we hope it’s yes. Suppose it is. Then think what has happened. You now know something no one else in the world does. It might not be important. It might not be of interest to another soul. But it’s all yours. I suspect there is just as much elation as Wiles experienced.

I don’t think it can be significantly different from what a musician feels when she’s composed a symphony or a mechanic when a confusing problem falls to his expertise. A mathematician in Math Is Murder describes the feeling.

Now imagine the joy evaporating in an instant when you discover an error in your argument. I remember one paper I submitted for publication with a colleague. It was in the refereeing process when I discovered an error. Through late night phone calls, my colleague and I worked to find a fix. Alas, we could not, because the theorem simply was not true. The answer to the question we had asked was “no,” not the “yes” we had originally thought, and we had to withdraw the paper.

I’ve been involved in the development of hundreds of theorems, perhaps as many as a thousand. Most of them I no longer can remember. But I have never forgotten the one time a paper had to be recalled.

But, despite the potential pitfalls, I still look for theorems I can prove. Because the thrill of success is impossible to describe.

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The Fourth Grade Syndrome

8/18/2018

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A great injustice occurred when I was in the fourth grade. Some irascible classmate tossed a purloined eraser at our teacher’s back as she applied chalk to the blackboard. There was general agreement on the appropriateness of the action since the teacher was not beloved. The adult me recognizes the unseemliness of it, but the feelings of the ten-year-old me were conflicted.

It’s interesting that this represented a major transgression in those innocent days. We had no drug problems of which I was aware. We had incorrigible kids, but no gangs. We did not worry about a shooter mowing us down, although the occasional atomic bomb was a concern. So the eraser toss was a significant juvenile crime. Today the police might be called. Back then punishment was applied locally.

The teacher, as you might imagine, was not pleased. She demanded a name. The culprit was to be revealed. Memory loss swept the room. Actually, I think very few of us knew who was responsible. There was no response to her demands.

Had the perpetrator been discovered, the punishment would have been after school detention. Since no one could pinpoint the evil doer, our teacher decreed the entire class should remain beyond normal school hours.

The entire class! We all were to be punished because of what one person did. I suppose there was some justice there, since no one was willing to squeal. But it still seemed wrong. And it still does. I call it the Fourth Grade Syndrome.

The Fourth Grade Syndrome remains popular. The story, true or not, of someone on welfare driving a Cadillac justifies attempts to censure everyone on welfare. One person, or even a threat of one, committing voter fraud generates a crackdown on huge groups of legitimate voters. A small number of thieves in department stores triggers extra security on a single class of citizens.

One runs into the Fourth Grade Syndrome in a variety of situations. Keep watch for when it appears and recognize it for what it is. Then search for the reasoning behind its application. With all the examples I can conjure where I think its use in inappropriate, it is a method for achieving and/or maintaining power.

At one point I would have declared that the Syndrome has no validity at any time. But as so often happens as I age, I find there are few good rules, that is, rules that work all the time.

There are situations where I find the Syndrome to be beneficial for maximizing the public good.

For example, very few of the millions of passengers that board planes carry bombs or guns or box cutters. But some do, and permitting that to happen can have devastating results. So we all must be punished, and most of us understand. Thus, we endure the annoyance, cost and lost time of security checks in order to feel comfortable entrusting our lives to a hunk of heavy material that can leave the ground under the guidance of highly trained individuals.

A less publicly accepted use of the Syndrome is the requirement of a background check before one is allowed to purchase a firearm. The number of abusers of firearms is huge, as attested to by the proliferation of tens of thousands of murders, accidents and suicides by gun every year. While this is small compared to the total number of gun owners in our country, it is not as insignificant as the number of plane bombers. So, yes, it’s reasonable the Syndrome should be employed, and all potential purchasers should be “punished” by having to undergo a background check (not a very severe punishment, I might add). The debate is out there, but I come down strongly on the side of universal checks because it benefits the public. Most of our citizenry agrees.

I’ve tried to gain an understanding of when it’s reasonable to institute the Syndrome and when it is not, and I have no solid answers.

It seems to me it’s okay if the public’s well-being is enhanced, all are inconvenienced equally, and there is general acceptance of its benefits.

And it appears to be as wrong as it can be when its motivation is gaining and keeping power.

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Columnists—and a Blog Shift

8/11/2018

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These days of the internet allow anyone to become a columnist. A few, ones who know how to write, are worth reading. The subjects are many: movies, books, theater, restaurants, TV, sports to name but a few.

Those that interest me the most comment on the national and world political scenes. At this time of institutional stress both in our own land and internationally, I read with a desperation that pleads for sanity in a time when sanity seems impossibly remote.

I place political columnists in three categories, two of which are uninteresting because I can almost always predict what they’ll say given the headline above the column.

The first of these two are pundits whose beliefs are antithetical to mine. Oh, how angry they make me! I seethe as I read them. It’s clear they’re jerks whose views are based in unreality. You understand there are those people, right, no matter what your own philosophy is? Those who don’t think like you have no rational insights. So why do I read them? There are three reasons. First, it’s because recognizing how foolish they are stirs me to righteous anger, which feels so good. Second, incredibly, these poor thinking individuals often are excellent wordsmiths. Finally, very occasionally, and it pains me to say this, something they say makes me consider things in different ways, makes me realize I don’t have all the answers. I usually read these columns first. It’s like eating the broccoli before getting to enjoy the ice cream.

The ice cream comes from the second uninteresting category, those columnists who are thinking clearly, that is, they agree with me. When everything is going bad in the world, here are people telling me the way I’m looking at things is not only correct, but is on the side of the angels. Sure, I know what they’ll say by looking at the headline, just like with that OTHER group, but it’s okay in this case because what is being written makes so much sense. And they do such a good job of mastering the written word.

I learn very little from either of these two categories, which brings me to the final one, the one I enjoy the most. The one where the headline doesn’t allow me to know what’s coming because the columnist is full of surprises. It is from them I learn the most. It is they who make me think the most. If I were a columnist, this is the class I’d want to be in.

Which is the perfect segue. I have now produced 35 postings related at least tangentially to the act of writing. And frankly, I’m running out of ideas. You have been kind to me. I tend to get anywhere from 60 to 90 views in average weeks. Once I came close to 150. That was the one about librarians, without a doubt one of my better efforts. I believe it was forwarded and that accounts for the high number. You have been a faithful audience to put up with my pontification when I have so little real knowledge and experience in the writing area.

It is tempting to say this has been a good run, an interesting experience, and a source of occasional gratification—so let’s call it quits.

I have been encouraged by exactly one person to continue the blog, still occasionally including thoughts on writing, but expanding the subject material. My immediate reaction was no one would care an iota about whatever ramblings I might produce, and I suspect that’s the case.

However, the idea appeals. Just for the fun of it, I jotted down several possible subjects. In short order I had 28, and I hadn’t even given the matter any real thought.
It’s scary to consider such an adventure. I’m an expert on almost nothing. What I do have is a long life during which I’ve experienced much of interest (to me) and had the time to contemplate and develop views in a number of areas.

So I’m going to give it a shot. I hope you’ll like some of what I’ll do. It’s not my intention to be overly controversial (no guarantees though), but rather to provide food for thought or enjoyment or both. If I succeed, wonderful. If I fail, it won’t be the first time.

No matter what, I feel so fortunate and honored that you have tuned in for as long as you have.

Thank you.

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Comics—Or Not?

8/4/2018

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Oh, how I loved comic books! There was a store directly across the street from my elementary school that sold such grownup items as cigarettes and magazines along with the much more child accessible candies, gum, soda—and comic books.

I suppose some of the older children attempted to purchase cigarettes, but I doubt it because Tom, the city policeman who patrolled that area, knew everyone by name and it would have been hard to put one over on him.

The store was owned by a married couple. I still can picture them, both overweight, he sitting on a stool near the cash register at the front, she on another at the back mostly hidden behind the crowded articles for sale. I can’t recall either ever moving and wondered if they stayed there overnight. We called him Izzy. I suppose that was his name. In no way was it meant to be disrespectful and I don’t think he considered it to be. Addressing her would have been a problem. Was it Mrs. Izzy or was there a hidden appellation waiting to be discovered? The problem did not arise, however, because there was never any communication with her.

I read such enlightened literature sold at Izzy’s as Superman, Batman, and Archie. When I felt it was time for a new volume to appear I’d stop daily at Izzy’s and say, “Is the new Superman in?” Since my inquiries started about a week before it was really due, Izzy usually responded in the negative. He seemed amused by my persistence. He was unfailingly pleasant, and in later life I wondered how he and his wife endured what must have been a difficult existence.

I remember one issue of Superman showed the superhero closing in on Hitler. I wondered how that was possible because I did know (I really did) that he wasn’t real and who knew when Hitler would fall. Actually, turns out Superman did know. The next issue had Hitler taken down and about the same time Germany surrendered and the real Hitler was dead.

Maturity has afforded many opportunities to make mistakes. One of mine was the tossing of all my comic books as I assisted my mother in moving from a home, seized by the government for “progress,” to an apartment. I think they might have fetched a minor fortune these days.

I haven’t read a comic book in decades. As far as I know, none of my acquaintances has. So imagine my surprise when I caught my wife with one spread before her. Hers differed from those of my youth. For one thing, the cover was hardback, just like a regular book. And the dialog was at a significantly higher level than “Shazam!”

“Reading comics, are you,” I said with a smile that did not hide the tone of derision.

“Not a comic book,” came the sharp retort. “They’re called graphic novels.” I gathered it was a new form of literature.

How wrong I was, at least about the “new.” I googled the term and discovered from Wikipedia there is a long history both in the United States and abroad of various forms of this media. A quick scan of reviews of several graphic novels indicates subjects that parallel traditional writings. They can be huge in length. One was noted to be 600 pages! It’s interesting that the reviews consider the caliber of both the author’s writing and the artist’s drawing.

I can’t speak much about this type of medium because it doesn’t appeal to me, so I haven’t given it a fair chance.

But any smugness on my part has evaporated since, in a recent journal published by the Sigma Xi science society, there was an article about the effectiveness of the graphic approach to presenting sophisticated notions from physics. Not a novel in this case, of course, but a serious scientific introduction to difficult ideas. The article had a one-page sample that I read. I am forced to admit it was an effective method for education.

So yet again I have to admire the creativity and genius of those searching for unique ways to express themselves.

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Why?

I Am a Mathematician

The Fourth Grade Syndrome

Columnists—and a Blog Shift

Comics—Or Not?

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